Critical analysis for nonlinear oscillations by least square HPM
Abstract In this study, a novel adapted homotopy perturbation method (HPM) is used to treat the nonlinear phenomena of free vibration in a system with one degree of freedom. This adaptation involves the integration of HPM with a least-squares optimizer, resulting in a hybrid method called the least...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-01-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-51706-3 |
| _version_ | 1797350014291279872 |
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| author | Muhammad Rafiq Muhammad Kamran Hijaz Ahmad Afis Saliu |
| author_facet | Muhammad Rafiq Muhammad Kamran Hijaz Ahmad Afis Saliu |
| author_sort | Muhammad Rafiq |
| collection | DOAJ |
| description | Abstract In this study, a novel adapted homotopy perturbation method (HPM) is used to treat the nonlinear phenomena of free vibration in a system with one degree of freedom. This adaptation involves the integration of HPM with a least-squares optimizer, resulting in a hybrid method called the least square homotopy perturbation method (LSHPM). The LSHPM is tested on various nonlinear problems documented in the existing literature. To evaluate the effectiveness of the proposed approach, the identified problems are also tackled using HPM and the MATLAB built-in function bvp5c, and then the results are compared with those obtained using LSHPM. In addition, a comparative analysis is carried out with the results of the AG method as found in the literature. The results show that LSHPM is a reliable and efficient method suitable for solving more complicated initial value problems in the fields of science and engineering. |
| first_indexed | 2024-03-08T12:39:40Z |
| format | Article |
| id | doaj.art-a6f10f9dfcee4d3ea121b6a906436359 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-08T12:39:40Z |
| publishDate | 2024-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-a6f10f9dfcee4d3ea121b6a9064363592024-01-21T12:16:39ZengNature PortfolioScientific Reports2045-23222024-01-0114111410.1038/s41598-024-51706-3Critical analysis for nonlinear oscillations by least square HPMMuhammad Rafiq0Muhammad Kamran1Hijaz Ahmad2Afis Saliu3Department of Mathematics, COMSATS University IslamabadDepartment of Mathematics, COMSATS University IslamabadDepartment of Mathematics, Faculty of Science, Islamic University of MadinahDepartment of Mathematics, University of the GambiaAbstract In this study, a novel adapted homotopy perturbation method (HPM) is used to treat the nonlinear phenomena of free vibration in a system with one degree of freedom. This adaptation involves the integration of HPM with a least-squares optimizer, resulting in a hybrid method called the least square homotopy perturbation method (LSHPM). The LSHPM is tested on various nonlinear problems documented in the existing literature. To evaluate the effectiveness of the proposed approach, the identified problems are also tackled using HPM and the MATLAB built-in function bvp5c, and then the results are compared with those obtained using LSHPM. In addition, a comparative analysis is carried out with the results of the AG method as found in the literature. The results show that LSHPM is a reliable and efficient method suitable for solving more complicated initial value problems in the fields of science and engineering.https://doi.org/10.1038/s41598-024-51706-3 |
| spellingShingle | Muhammad Rafiq Muhammad Kamran Hijaz Ahmad Afis Saliu Critical analysis for nonlinear oscillations by least square HPM Scientific Reports |
| title | Critical analysis for nonlinear oscillations by least square HPM |
| title_full | Critical analysis for nonlinear oscillations by least square HPM |
| title_fullStr | Critical analysis for nonlinear oscillations by least square HPM |
| title_full_unstemmed | Critical analysis for nonlinear oscillations by least square HPM |
| title_short | Critical analysis for nonlinear oscillations by least square HPM |
| title_sort | critical analysis for nonlinear oscillations by least square hpm |
| url | https://doi.org/10.1038/s41598-024-51706-3 |
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